1989 APMO Problems
Let be positive real numbers, and let
Prove that the equation
has no solutions in integers except .
Let be three points in the plane, and for convenience, let , . For and , suppose that is the midpoint of , and suppose that is the midpoint of . Suppose that and meet at , and that and meet at . Calculate the ratio of the area of triangle to the area of triangle .
Let be a set consisting of pairs of positive integers with the property that . Show that there are at least
triples such that , , and belong to .
is a strictly increasing real-valued function on reals. It has inverse . Find all possible such that for all .